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The Biggest Problem with Your Pricing Model is Your Reserving Model - - PowerPoint PPT Presentation

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The Biggest Problem with Your Pricing Model is Your Reserving Model Southwest Actuarial Forum June 3rd Presenter: Chris Gross Gross Consulting The Pricing Problem Estimate discounted value of ultimate claim costs and expenses Estimate

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The Biggest Problem with Your Pricing Model is Your Reserving Model

Southwest Actuarial Forum June 3rd Presenter: Chris Gross

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The Pricing Problem

  • Estimate discounted value of ultimate claim

costs and expenses

  • Estimate differences across available rating

characteristics

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The (incomplete) Solution

  • Build models based on the current diagonal
  • nly
  • Build models based on a common age of

development

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(incomplete) Treatment of Loss Development

  • Develop all losses with a factors based on age
  • Reduce premium/exposure based on age
  • Include policy effective date as a variable
  • Only use the process to rank policies
  • Generally assumes all development is the

same (wrong!)

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The Mix Problem… An Example

  • Two classes of business

– Class 1.

  • Faster developing
  • Lower ultimate loss ratio (60%)

– Class 2

  • Slower developing
  • Higher ultimate loss ratio (90%)
  • Class 2 has always been there, but only

recently started growing significantly

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 Percent of Ultimate Yr of Development Class 1 Class 2

Different Development

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Loss as of: Year Premium Age 1 Age 2 Age 3 Age 4 Age 5 Age 6 Age 7 Age 8 Age 9 Age 10 2006 105 7.53 20.40 32.67 43.49 52.72 58.08 61.20 62.36 63.28 64.50 2007 105 8.06 20.72 32.65 43.52 54.68 60.16 63.87 64.15 63.71 2008 105 6.48 19.23 30.80 42.47 52.70 58.32 60.99 62.91 2009 105 7.21 19.21 30.81 42.44 52.93 59.64 61.78 2010 105 7.43 21.88 34.36 43.89 53.76 59.81 2011 105 6.76 19.19 33.07 43.90 54.42 2012 105 7.11 18.49 30.01 40.40 2013 120 8.44 22.18 37.25 2014 140 8.65 25.87 2015 160 9.81

The Triangle

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2006 2.709 1.602 1.331 1.212 1.102 1.054 1.019 1.015 1.019 2007 2.571 1.576 1.333 1.256 1.100 1.062 1.005 0.993 2008 2.967 1.602 1.379 1.241 1.107 1.046 1.031 2009 2.666 1.604 1.378 1.247 1.127 1.036 2010 2.944 1.570 1.277 1.225 1.113 2011 2.840 1.724 1.327 1.239 2012 2.602 1.622 1.346 2013 2.630 1.679 2014 2.990 Last 3 2.740 1.675 1.317 1.237 1.115 1.048 1.018 1.004 1.019 Cumulative 9.108 3.324 1.984 1.506 1.218 1.092 1.042 1.023 1.019

Development Factors

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40.0% 45.0% 50.0% 55.0% 60.0% 65.0% 70.0% 75.0% 80.0% Estimate Actual

True Loss Ratio vs Estimate

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Potential Differences

  • Industry classification
  • Geography
  • Deductible/Limit Profile
  • Size of account
  • Type of Claims
  • Etc.
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Challenges to Building a Complete Model

  • An age old problem

– Loss development occurs over time, mature periods are old – Immature claims contain information

  • Many facets of loss development
  • Helpful to concentrate on a single time‐step

(e.g. beginning of quarter to end of quarter)

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Data

Financial Data Exposure Characteristics Beginning Case Reserve Type Ending Case Reserve Product Payment in Period ZIP Code Timing Data Claim Characteristics Accident Quarter Loss Cause Report Quarter Loss Cause ‐ Detail Valuation Quarter

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Claim activity from the beginning of the quarter to the end of the quarter

Did the Claim Close? Does the Claim Have a New Value? Is there a Payment? What is the New Value? How much is the Payment?

Arrows indicate dependency on other results

A number of available claim or exposure characteristics may have predictive value for any of these questions.

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Probability of a Claim Closing

  • Base probability of

71%

  • Modification of this

probability by various claim characteristic values that were found to have predictive value

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Close Probability – Claim Age

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Close Probability – Loss Cause

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Close Probability – Accident Quarter

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Close Probability ‐ Product

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Probability of Change in Value (Given Not Closed)

  • Base probability of

37%

  • 4 characteristics

found to be predictive

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New Claim Value (Given Changed but Not Closed)

  • Base factor of 1.98 to

beginning case reserve

  • Modification to this

linear relationship, as well as five additional predictive characteristics

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New Claim Value ‐ Case Reserve

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New Claim Value – Loss Cause

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New Claim Value – ZIP Code

10 20 30 40 50 60 70 80 90 100 0.6 ‐ 0.7 0.7 ‐ 0.8 0.8 ‐ 0.9 0.9 ‐ 1.0 1.0 ‐ 1.1 1.1 ‐ 1.2 1.2 ‐ 1.3 1.3 ‐ 1.4 1.4 ‐ 1.5 1.5 ‐ 1.6 1.6 ‐ 1.7 Number of ZIP Codes Factor

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Bringing it together

  • Simulation can be used to project activity in

the next quarter

  • It is necessary to project not only the

predictive relationships, but also the residual error term.

  • Chain through quarters using information

from the previous simulated quarter.

  • Store results, preferably at the claim level.
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Simulate Going Forward

  • Claim Development

– Start with current inventory of open claims – For each open claim simulate a number of potential outcomes for the next time‐step (using the claims’ characteristics) – For those simulated claim‐paths that are still open simulate forward another time‐step. – Continue until all simulated claim‐paths are closed

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Claim 1

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Claim 2

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Claim 3

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0.2 0.4 0.6 0.8 1

Grand Total

Probability distribution of total payments

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0.2 0.4 0.6 0.8 1

Grand Total

Mean of total payments

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0.2 0.4 0.6 0.8 1

Grand Total

Current case reserves

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0.2 0.4 0.6 0.8 1

Product 1

0.2 0.4 0.6 0.8 1

Product 2

0.2 0.4 0.6 0.8 1

Product 3

0.2 0.4 0.6 0.8 1

Product 4

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0.2 0.4 0.6 0.8 1

Loss Cause 1

0.2 0.4 0.6 0.8 1

Loss Cause 2

0.2 0.4 0.6 0.8 1

Loss Cause 3

0.2 0.4 0.6 0.8 1

Loss Cause 4

0.2 0.4 0.6 0.8 1

Loss Cause 5

0.2 0.4 0.6 0.8 1

Loss Cause 6

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Emergence

  • After simulating claim development to

ultimate, model emergence

  • Frequency
  • Severity
  • Report Lag
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Claim Emergence

Report Lag Ultimate Claim Severity Claim Frequency Claim Development Simulation

Arrows indicate dependency on other results

A number of exposure characteristics may have predictive value for any of these questions.

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Emergence Simulation

  • Use written policies (w/ characteristics)

simulate remaining emergence.

  • Generating loss date within this process allows

accident period calculations

  • Also get losses associated with unearned

premium

  • Inforce loss ratio distribution.
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  • Capital Insurance Group
  • Reasons for interest in the approach

– Validate ultimate selections made from traditional triangle‐based methods – Insights that can be gained by applying predictive modeling to reserving – Triangle segmentation ideas – Support pricing predictive modeling by using estimated ultimate claims as the target variable

Case Study ‐ Background

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Case Study ‐ Background

  • Began the process in Q4 of 2015
  • Analyzed Q4 2014 (1 Year Lag) to be able to

compare against traditional approach

  • Involved three individuals in the actuarial

department

  • Single line of business
  • Longer‐tailed LOB
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Learning Curve

  • Chris came for an initial in‐house training

session

  • Met every couple of weeks to answer

questions on software and get valuable feedback on progress

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Learning Curve

  • Main challenge was getting all the data into an

acceptable format and gaining familiarity of the software functionality

  • Easy to use and really fast automated results

after getting over the initial learning curve hump

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Case Study ‐ Process

  • Organized data
  • Built and refined the predictive models
  • Simulated development and emergence
  • Analyzed output vs. current reserve model vs.

actual development

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Case Study – Selected Highlights

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Case Study– Selected Highlights

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Case Study– Selected Highlights

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Case Study – Overall Impressions

  • Challenges

– Reconciliation with other analysis

  • Value

– Depth of information available – Statistically significant segmentation – Visual aids for decision making are an invaluable part of the process – Easy to evaluate performance of one model iteration to the next

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Case Study – Thoughts for the future

  • Reserving
  • Pricing
  • Other
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Additional Comparisons of “Traditional” Predictive Modeling for Pricing vs. Claim Life Cycle Model

  • 3 other real examples
  • Using the same rating variables
  • Only difference is use of CLCM ultimate vs

Case‐Incurred.

  • Compared modeled loss ratio by policy from

the current inforce book.

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Example 1

CLCM Based Case Incurred Based

Modeled Loss Ratios of Inforce Book

Policy No difference

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Example 2

CLCM Based Case Incurred Based

Modeled Loss Ratios of Inforce Book

Policy No difference

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Example 3

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Some Observed Differences

  • Geography
  • Industry Classification
  • Size of Account
  • Agency
  • Deductible/Limit
  • Year Built
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Conclusion

  • Reserve development matters for pricing!
  • Different exposures develop differently!
  • Models that do not reflect these differences

will be inferior!